Your job isn't decision making but you can make sure management is fully aware of what they are dealing with. Outline major problems that you keep running across, you mention highly coupled platforms, that usually means changes in one system can have negative affects on another, and may not happen right away.
The big trade-offs for ignoring tech debt are software quality, system health and speed of development. Those things will get worse with time. If you bring up facts with evidence, on how those are poor because of the tech debt, it could help. Better yet, align tech debt with product strategy. For example, you know the product strategy is to do more X and system 1 is primarily involved with X but changes impact systems 2 and 3. Propose untangling system 1 from 2 and 3 as part of the effort with improving/building more X features. It really pays off when system 1 is loosely coupled from others and can evolve on it's own.
A common theme I've seen from some developers is basically to toss out the old system and build a new one. This usually never works. You probably need to start small with minor refactors to improve things and build credibility that refactoring is a path towards a better system.
When it comes down to it though, if management listens and mostly just ignores your advice, wait for the next failure and after it is resolved, gently (not "I told you so") bring it up again that maybe it could have been prevented.